Developmental Mathematics (9th Edition)
9th Edition
ISBN: 9780321997173
Author: Marvin L. Bittinger, Judith A. Beecher
Publisher: PEARSON
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Chapter O, Problem 30DE
To determine
To calculate: The value of the expression
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Question 3
over a field K.
In this question, MË(K) denotes the set of n × n matrices
(a) Suppose that A Є Mn(K) is an invertible matrix. Is it always true that A is
equivalent to A-¹? Justify your answer.
(b) Let B be given by
8
B = 0 7 7
0 -7 7
Working over the field F2 with 2 elements, compute the rank of B as an element
of M2(F2).
(c) Let
1
C
-1 1
[4]
[6]
and consider C as an element of M3(Q). Determine the minimal polynomial
mc(x) and hence, or otherwise, show that C can not be diagonalised.
[7]
(d) Show that C in (c) considered as an element of M3(R) can be diagonalised. Write
down all the eigenvalues. Show your working.
[8]
16. Solve the given differential equation:
y" + 4y sin (t)u(t 2π),
-
y(0) = 1, y'(0) = 0
Given,
1
(x² + 1)(x²+4)
1/3
-1/3
=
+
x²+1 x² +4
Send your answer in
pen and paper don't r
eputed ur self down
Don't send the same
previous answer that
was Al generated
Don't use any Al tool
show ur answer in pe
n and paper then take
R denotes the field of real numbers, Q denotes the field of rationals, and
Fp denotes the field of p elements given by integers modulo p. You may refer to general
results from lectures.
Question 1
For each non-negative integer m, let R[x]m denote the
vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m.
x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent
(a) Let vi = x, V2 =
list in R[x] 3.
(b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4)
is a basis of R[x] 3.
[8]
[6]
(c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a
linear map.
[6]
(d) Write down the matrix for the map ƒ defined in (c) with respect to the basis
(2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3.
[5]
Chapter O Solutions
Developmental Mathematics (9th Edition)
Ch. O - Prob. 1DECh. O - Prob. 2DECh. O - Prob. 3DECh. O - Prob. 4DECh. O - Prob. 5DECh. O - Prob. 6DECh. O - Prob. 7DECh. O - Prob. 8DECh. O - Prob. 9DECh. O - Prob. 10DE
Ch. O - Prob. 11DECh. O - Prob. 12DECh. O - Prob. 13DECh. O - Prob. 14DECh. O - Prob. 15DECh. O - Prob. 16DECh. O - Prob. 17DECh. O - Prob. 18DECh. O - Simplify.
19.
Ch. O - Prob. 20DECh. O - Prob. 21DECh. O - Prob. 22DECh. O - Prob. 23DECh. O - Prob. 24DECh. O - Prob. 25DECh. O - Find the conjugate.
26.
Ch. O - Prob. 27DECh. O - Prob. 28DECh. O - Prob. 29DECh. O - Prob. 30DECh. O - Prob. 31DECh. O - Prob. 32DECh. O - Prob. 33DECh. O - Prob. 34DECh. O - Prob. 36DECh. O - Prob. 37DECh. O - Prob. 38DECh. O - Prob. 1ESCh. O - Prob. 2ESCh. O - Prob. 3ESCh. O - Prob. 4ESCh. O - Prob. 5ESCh. O - Prob. 6ESCh. O - Prob. 7ESCh. O - Prob. 8ESCh. O - Prob. 9ESCh. O - Prob. 10ESCh. O - Prob. 11ESCh. O - Prob. 12ESCh. O - Prob. 13ESCh. O - Prob. 14ESCh. O - Prob. 15ESCh. O - Prob. 16ESCh. O - Prob. 17ESCh. O - Prob. 18ESCh. O - Prob. 19ESCh. O - Prob. 20ESCh. O - Prob. 21ESCh. O - Prob. 22ESCh. O - Prob. 23ESCh. O - Prob. 24ESCh. O - Prob. 25ESCh. O - Prob. 26ESCh. O - Prob. 27ESCh. O - Prob. 28ESCh. O - Prob. 29ESCh. O - Prob. 30ESCh. O - Prob. 31ESCh. O - Prob. 32ESCh. O - Prob. 33ESCh. O - Prob. 34ESCh. O - Prob. 35ESCh. O - Prob. 36ESCh. O - Prob. 37ESCh. O - Prob. 38ESCh. O - Prob. 39ESCh. O - Prob. 40ESCh. O - Prob. 41ESCh. O - Prob. 42ESCh. O - Prob. 43ESCh. O - Prob. 44ESCh. O - Prob. 45ESCh. O - Prob. 46ESCh. O - Prob. 47ESCh. O - Prob. 48ESCh. O - Prob. 50ESCh. O - Prob. 51ESCh. O - Prob. 52ESCh. O - Prob. 53ESCh. O - Prob. 54ESCh. O - Prob. 55ESCh. O - Prob. 56ESCh. O - Prob. 57ESCh. O - Prob. 58ESCh. O - Prob. 59ESCh. O - Prob. 60ESCh. O - Prob. 61ESCh. O - Prob. 62ESCh. O - Prob. 63ESCh. O - Prob. 64ESCh. O - Prob. 65ESCh. O - Prob. 66ESCh. O - Prob. 67ESCh. O - Prob. 68ESCh. O - Prob. 69ESCh. O - Prob. 70ESCh. O - Prob. 71ESCh. O - Prob. 72ESCh. O - Prob. 73ESCh. O - Prob. 74ESCh. O - Prob. 75ESCh. O - Prob. 76ESCh. O - Prob. 77ESCh. O - Prob. 78ESCh. O - Prob. 79ESCh. O - Prob. 80ESCh. O - Prob. 81ESCh. O - Prob. 82ESCh. O - Prob. 83ESCh. O - Prob. 84ESCh. O - Prob. 85ESCh. O - Prob. 86ESCh. O - Prob. 87ESCh. O - Prob. 88ESCh. O - Prob. 89ESCh. O - Prob. 90ESCh. O - Prob. 91ESCh. O - Prob. 92ESCh. O - Prob. 93ESCh. O - Prob. 94ESCh. O - Prob. 95ESCh. O - Prob. 96ESCh. O - Prob. 97ESCh. O - Prob. 98ESCh. O - Prob. 99ESCh. O - Prob. 100ESCh. O - Prob. 101ESCh. O - Prob. 102ESCh. O - Prob. 103ESCh. O - Prob. 104ESCh. O - Prob. 105ESCh. O - Prob. 106ESCh. O - Prob. 107ESCh. O - Prob. 108ESCh. O - Prob. 109ESCh. O - Prob. 110ESCh. O - Prob. 111ESCh. O - Prob. 112ESCh. O - Prob. 113ESCh. O - Prob. 114ES
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